Search results for Theoretical Physics and Mathematical Physics

17 - Methods of Scattering Theory
from Part III - Mathematical Methods and Analytic Constructions
Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
Book:

Causal Fermion Systems

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15 November 2025

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23 October 2025, pp 309-319
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Summary

The mass oscillation property is proved in Minkowski space using methods of scattering theory.

16 - Fourier Methods
from Part III - Mathematical Methods and Analytic Constructions
Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
Book:

Causal Fermion Systems

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15 November 2025

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23 October 2025, pp 296-308
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Summary

Fourier methods for the analysis are developed and used for the analysis of the kernel of Green’s operators, the causal fundamental solution and the kernel of the fermionic projector.

19 - Methods of Microlocal Analysis
from Part III - Mathematical Methods and Analytic Constructions
Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
Book:

Causal Fermion Systems

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15 November 2025

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23 October 2025, pp 328-350
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The Hadamard expansion of the kernel of the fermionic projector is derived. The connection to the light-cone expansion and the wave front set is worked out.

7 - The Euler–Lagrange Equations
from Part II - Causal Fermion Systems: Fundamental Structures
Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
Book:

Causal Fermion Systems

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15 November 2025

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23 October 2025, pp 148-155
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The Euler–Lagrange equations for causal variational principles are derived, and their general structure is discussed.

15 - Functional Analytic Methods in Spacetime
from Part III - Mathematical Methods and Analytic Constructions
Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
Book:

Causal Fermion Systems

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15 November 2025

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23 October 2025, pp 279-295
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Summary

A functional analytic method is developed, which gives rise to a canonical decomposition of the Dirac solution space into two subspaces, even in a time-dependent situation.

Contents
Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
Book:

Causal Fermion Systems

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15 November 2025

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23 October 2025, pp vii-xii
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2 - Mathematical Preliminaries
from Part I - Physical and Mathematical Background
Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
Book:

Causal Fermion Systems

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15 November 2025

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23 October 2025, pp 21-58
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Summary

We summarize some mathematical preliminaries that we believe are important for studying causal fermion systems.

13 - Methods of Hyperbolic Partial Differential Equations
from Part III - Mathematical Methods and Analytic Constructions
Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
Book:

Causal Fermion Systems

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15 November 2025

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23 October 2025, pp 243-267
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Summary

The well-posedness of the Cauchy problem for linear symmetric hyperbolic systems is proven, and consequences are worked out.

3 - Elements of Operator Theory
from Part I - Physical and Mathematical Background
Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
Book:

Causal Fermion Systems

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15 November 2025

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23 October 2025, pp 59-67
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Summary

We introduce some material from functional analysis that will be needed later in this book.

Part II - Causal Fermion Systems: Fundamental Structures
Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
Book:

Causal Fermion Systems

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15 November 2025

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23 October 2025, pp 91-92
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10 - Positive Functionals
from Part II - Causal Fermion Systems: Fundamental Structures
Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
Book:

Causal Fermion Systems

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15 November 2025

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23 October 2025, pp 190-198
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Summary

Positive functionals arising from causal variational principles are derived and discussed.

8 - The Linearized Field Equations
from Part II - Causal Fermion Systems: Fundamental Structures
Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
Book:

Causal Fermion Systems

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15 November 2025

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23 October 2025, pp 156-170
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Summary

The linearized field equations for causal variational principles are derived, and their general structure is discussed.

Preface
Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
Book:

Causal Fermion Systems

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15 November 2025

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23 October 2025, pp xiii-xiv
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Part IV - Applications and Outlook
Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
Book:

Causal Fermion Systems

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15 November 2025

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23 October 2025, pp 351-352
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21 - Basics on the Continuum Limit
from Part IV - Applications and Outlook
Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
Book:

Causal Fermion Systems

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15 November 2025

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23 October 2025, pp 366-378
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Summary

An introduction to and overview of the continuum limit analysis of the causal action principle is given.

References
Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
Book:

Causal Fermion Systems

Published online:

15 November 2025

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23 October 2025, pp 391-397
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How to Use This Book
Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
Book:

Causal Fermion Systems

Published online:

15 November 2025

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23 October 2025, pp xv-xvi
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18 - Methods of Perturbation Theory
from Part III - Mathematical Methods and Analytic Constructions
Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
Book:

Causal Fermion Systems

Published online:

15 November 2025

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23 October 2025, pp 320-327
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Summary

The perturbation theory for the Green’s operators and the kernel of the fermionic projector is developed.

Notation Index: In Order of Appearance
Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
Book:

Causal Fermion Systems

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15 November 2025

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23 October 2025, pp 398-400
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On the degree-two part of the associated graded of the lower central series of the Torelli group
Part of
- Special aspects of infinite or finite groups
QUENTIN FAES, GWÉNAËL MASSUYEAU, MASATOSHI SATO
Journal:

Mathematical Proceedings of the Cambridge Philosophical Society , First View

Published online by Cambridge University Press:

20 October 2025, pp. 1-39
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We consider the associated graded $\bigoplus_{k\geq 1} \Gamma_k \mathcal{I} /\Gamma_{k+1} \mathcal{I} $ of the lower central series $\mathcal{I}\,=\,\Gamma_1 \mathcal{I}\supset \Gamma_2 \mathcal{I}\supset \Gamma_3 \mathcal{I} \supset \cdots$ of the Torelli group $\mathcal{I}$ of a compact oriented surface. Its degree-one part is well understood by D. Johnson’s seminal works on the abelianization of the Torelli group. The knowledge of the degree-two part $(\Gamma_2 \mathcal{I} / \Gamma_3 \mathcal{I})\otimes \mathbb{Q}$ with rational coefficients arises from works of S. Morita on the Casson invariant and R. Hain on the Malcev completion of $\mathcal{I}$. Here, we prove that the abelian group $\Gamma_2 \mathcal{I} / \Gamma_3 \mathcal{I}$ is torsion-free, and we describe it as a lattice in a rational vector space. As an application, the group $\mathcal{I}/\Gamma_3 \mathcal{I}$ is computed, and it is shown to embed in the group of homology cylinders modulo the surgery relation of $Y_3$-equivalence.

Theoretical Physics and Mathematical Physics

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26203 results in Theoretical Physics and Mathematical Physics

17 - Methods of Scattering Theory

Summary

16 - Fourier Methods

Summary

19 - Methods of Microlocal Analysis

Summary

7 - The Euler–Lagrange Equations

Summary

15 - Functional Analytic Methods in Spacetime

Summary

Contents

2 - Mathematical Preliminaries

Summary

13 - Methods of Hyperbolic Partial Differential Equations

Summary

3 - Elements of Operator Theory

Summary

Part II - Causal Fermion Systems: Fundamental Structures

10 - Positive Functionals

Summary

8 - The Linearized Field Equations

Summary

Preface

Part IV - Applications and Outlook

21 - Basics on the Continuum Limit

Summary

References

How to Use This Book

18 - Methods of Perturbation Theory

Summary

Notation Index: In Order of Appearance

On the degree-two part of the associated graded of the lower central series of the Torelli group

Theoretical Physics and Mathematical Physics

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